What are the solutions to the equation 1+2x-3x^2+x^3=2x-3 ?

The solutions to the equation 1+2x-3x^2+x^3=2x-3 are x=-1,x=2

Find the zeros of 1+2x-3x^2+x^3=2x-3

The zeros of 1+2x-3x^2+x^3=2x-3 are x=-1,x=2

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1 + 2 x - 3 x^{2} + x^{3} = 2 x - 3

x = - 1, x = 2

Solution steps

1 + 2 x - 3 x^{2} + x^{3} = 2 x - 3

Move

3

to the left side

x^{3} - 3 x^{2} + 2 x + 4 = 2 x

Move

2 x

to the left side

x^{3} - 3 x^{2} + 4 = 0

Factor

x^{3} - 3 x^{2} + 4 : (x + 1) (x - 2)^{2}

(x + 1) (x - 2)^{2} = 0

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

x + 1 = 0 or x - 2 = 0

Solve

x + 1 = 0 : x = - 1

Solve

x - 2 = 0 : x = 2

The solutions are

x = - 1, x = 2

x^{3} - 3 x^{2} + 3 x - 1 = 0

x^{3} - 4 x^{2} - 4 x + 16 = 0

(x^{2} - 64)^{2} + (x^{2} + 5 x - 104)^{2} = 0

5 x^{3} - 7 x + 2

x^{5} - 2 x^{4} + 2 x^{3} - 4 x^{2} - 2 = 0

What are the solutions to the equation 1+2x-3x^2+x^3=2x-3 ?
The solutions to the equation 1+2x-3x^2+x^3=2x-3 are x=-1,x=2
Find the zeros of 1+2x-3x^2+x^3=2x-3
The zeros of 1+2x-3x^2+x^3=2x-3 are x=-1,x=2